Harnack Inequalities and Applications for Multivalued Stochastic Evolution Equations

TL;DR

This paper establishes Harnack inequalities and related properties for multivalued stochastic evolution equations, providing new bounds and insights into the behavior of their transition semigroups.

Contribution

It introduces novel Harnack inequalities for multivalued stochastic evolution equations using coupling and Girsanov methods, with applications to invariant measures and semigroup properties.

Findings

Proved Harnack inequalities for the transition semigroup.

Derived explicit bounds for the $L^p$-norm of the density.

Analyzed the concentration of invariant measures and semigroup properties.

Abstract

By the method of coupling and Girsanov transformation, Harnack inequalities [F.-Y. Wang, 1997] and strong Feller property are proved for the transition semigroup associated with the multivalued stochastic evolution equation on a Gelfand triple. The concentration property of the invariant measure for the semigroup is investigated. As applications of Harnack inequalities, explicit upper bounds of the $L^p$-norm of the density, contractivity, compactness and entropy-cost inequality for the semigroup are also presented.